'Space contains a number of qualities.It expands in all directions.It is without limits.It is uninterrupted, which means that a volume occupies a part of the void; and a void and volume make space.The great truth, the absolute truth, makes itself visible to our mind by means of the invisible.'

Georges Vantongerloo, quoted in his 'Reflections' written in The Hague, 1917. The first part published in no. 9/1 of the journal De Stijl in July 1918.

Spirale avec certaines taches was painted by the pioneering abstract artist, Georges Vantongerloo, in 1946. It issues from the mature part of his oeuvre when the artist was fully realising the far-reaching implications of his earliest artistic experiments and writings on concrete art. Writing to the former owner of the present work, the renowned Belgian architect Georges Baines in 1964, the artist states 'it took some time to comprehend that in 1917 my instincts were correct but not my understanding' (G. Baines, Georges Vantongerloo, 'The Influence of the Works of Wouters and the Origin of the First Abstract Works' (unpublished essay), 1981).

Born and educated in Antwerp yet exiled to Holland during the First World War, Vantongerloo became a founding contributor to the highly influential journal De Stijl as well as a signatory of the group's first manifesto. In late March 1918, the young Vantongerloo approached the editor of De Stijl, Theo van Doesburg, at his studio in Leiden with a notebook containing the beginnings of his 'Reflections', written in the preceding year, on the future of art and role of the artist. The content fascinated Van Doesburg and he agreed to publish the text under a new title 'Reflections by G. Vantongerloo' over the course of seven editions of the magazine up until 1920.

De Stijl's lasting influence on the development of Twentieth Century modern art and design cannot be overstated. Indeed, at the time, the journal was not simply the vehicle for Piet Mondrian's theories on art and Neo-Plasticism but also the mouthpiece for radical contemporary art across Western Europe. Among the renowned contributors, including Van Doesburg, Bart van der Leck and Piet Mondrian, Vantongerloo was the youngest and most progressive (Mondrian's junior by some 14 years), and his distinct involvement with the group is testament to his unrelenting desire for authenticity and universal truths within his own art.

From 1918 many of Vantongerloo's paintings paralleled the orthogonal grids of Mondrian, though he soon broke away from the limited palette of three primary colours espoused by Mondrian and Van der Leck to employ a chromatic range of seven hues including purple. Vantongerloo's unusual use of colour was in fact the main subject of the active correspondence which ensued between the two artists following Vantongerloo's first meeting with Mondrian in April 1920. After a brief spell in Brussels after the war, Theo van Doesburg informed Vantongerloo that Mondrian wished to make his acquaintance, and so Vantongerloo travelled to Paris en route to Menton on the French Riviera, where he had decided to make his home. It was an encounter which, despite their ideological differences, prompted a life-long friendship forged on their mutual dedication to abstraction in the search for universal values.

After Vantongerloo's move to Paris in 1928, where he initially stayed at Mondrian's home in the capital, both artists would become founding members of the Cercle et Carré group and later, Abstraction-Création; movements which upheld the concepts of 'Abstraction' and 'Constructivism' in opposition to the powerful influence of the Surrealist movement sweeping across Paris. Vantongerloo was elected vice-president of Abstraction-Création from 1931 - 1937, and was instrumental in the realisation of group exhibitions, as well as in the production of the eponymous pamphlet which published non-figurative work from members of the group, including Josef Albers, László Moholy-Nagy, Františzek Kupka and Jean Arp. This movement was crucial to the galvanisation of geometric and abstract art in the first half of the Twentieth Century and succeeded in bringing together a group of abstract artists from differing theoretical backgrounds.

Following the move to Paris and up until 1936, Vantongerloo established a unity of volumes, colours and planes within his paintings grounded on science and complex mathematical formulas. An approach so unique that Margit Staber has named Vantongerloo 'the inventor of the mathematical approach in art' (G. Brett (ed.), Force Fields, Phases of the Kinetic, exh. cat., Barcelona, 2000, p. 18). While these works retain the horizontal – vertical compositions akin to the De Stijl aesthetic, their underlying principles remain quite different. From 1937 however a dramatic shift occurred in Vantongerloo's painting which acted in total defiance to De Stijl's doctrine, namely the introduction of the curve. Indeed, when Mondrian was first informed of Vantongerloo's use of the curve in 1938 it was noted that he replied, 'I might have known' with a wry smile.

These new, dynamic lines serve to soften the austere constructions of his former paintings and release them from measurable geometric constraints. Reflecting upon this transition, the artist wrote to his close friend, the artist Max Bill: 'I have occupied myself and thought about art for many years but the history of the different aspects of curves has made me think that there are no rules in art, that is to say, each work has its own rules and if one repeats them one falls into dogma. Each work of art must be born with its own character' (G. Vantongerloo, 10 January 1947, quoted in M. Bill, (ed.) Georges Vantongerloo, exh. cat., London, 1962).

It was at this time that his works increasingly became concerned with the natural world and phenomena observed rather than hypothesised: 'One paints directly from nature' the artist explained, 'not in order to copy, but in an effort to penetrate the mystery of nature through observation and to express the feelings of grandeur received from the phenomenon observed' (G. Vantongerloo, 'Paintings, Sculptures, Reflections' in Problems of Contemporary Art, New York, Vol. V, 1948, p. 3). Liberated from the rectilinear confinements of a closed grid, the white ground of his works become 'a special theatre where the composition takes place' (G. Vantongerloo, letter to Max Bill 12 March 1945, quoted in M. Bill, (ed.), op. cit.). Compositions which, in their ever-growing free form, reveal themselves as 'idea patterns, sketches of the captured processes of nature...Vantongerloo in a sense produces new realities, reducing the invisible by mental process to aesthetic facts' (M. Bill, (ed.), ibid., p. 5).

It was by deducing these aesthetic facts that Vantongerloo was able to 'take a sounding of the incommensurable'. In other words, to perceive the immeasurable, infinite and intangible energies which underpin the universe. Though we are unable to perceive the infinite through our five senses, Vantongerloo explains, 'through discernment and deduction, through the subtlety of the sensibility and through science, man is able to approach the inconceivable' (G. Vantongerloo, 'To Perceive', 1957, quoted in G. Brett (ed.), op. cit., pp. 234 - 235).

Spirale avec certaines taches is a consummate example of Vantongerloo taking a 'sounding of the incommensurable'. Illustrating a multi-coloured filament in the form of a spiral surrounded by scattered constellations of spots / dots or points in varying sizes against a smooth white support, the work immediately recalls associations with the Fibonacci sequence and the golden spiral - mathematical principles which achieve balance and beauty in art yet which are to be found reproduced in the natural world in the form of nautilus shells, pinecones, seed heads and spiral galaxies. Nature was a constant source of wonder and insight for Vantongerloo but never a subject for his art, 'I have painted from nature – not the visible but what I feel, and it is not objective but what I consciously feel for form' (G. Vantongerloo, letter to Max Bill 1945, quoted in M. Bill, (ed.), op. cit.) Here, rather than representing nature itself, Vantongerloo gestures towards its fundamental structures and by extension, the infinite.

The spiral was a persistent motif in Vantongerloo's painting from 1946 – 1950, and his understanding of the sign also accords with Paul Klee's writings on the same subject in 1945. For Klee, the spiral is inextricably linked to a certain point, from which the spiral can either extend towards infinity or, in the opposite direction, follow a course of ever increasing retraction towards a central abyss (J - E. Grislain 'Métamorphoses de la ligne 1937 – 1950', Georges Vantongerloo 1886 – 1965, Un pionnier de la sculpture modern, exh. cat., Paris, 2007, p. 150). The point therefore embodies both the possibility of infinite expansion and retraction towards nothingness, a conceptualisation which looks back to Vantongerloo's earliest writings in his 'Reflections' of 1917: 'The point is the image of the infinitely great and infinitesimal, and contains all and nothing. [...] The point radiates on all sides and thus creates motion. As the point is the infinity of everything, the power of everything, and therefore all powerful, motion will be perpetual' (G. Vantongerloo, quoted in G. Maldonado, 'The curve in plastic arts: Art from surface to universe', Georges Vantongerloo: A Longing for Infinity, exh. cat., Madrid, 2009, p. 115).

Thus, the point and the spiral in Spirale avec certaines taches describe a conceptual oscillation between the finite and the infinite, dispersion and concentration, beginning and end. Becoming a 'stationary work[s] of endless movement' which Peter C. Marizo denotes as symbolic of Vantongerloo's oeuvre. It is as if, in presenting a dialectic without synthesis, Vantongerloo can allude to the endless metamorphosis which he understood as underlying creation itself: 'All creation undergoes a perpetual transformation. Therefore, there are no dimensions. But the riddle of creation presents us with a spectacle of beauty which moves us and expresses itself in art 'from' nature' (G. Vantongerloo, 'An Intimate Biography', 1961, quoted in Georges Vantongerloo. A traveling Retrospective Exhibition, Brussels, 1980, p. 54).

Later, Vantongerloo would become particularly fascinated by the atmospheric effects of the aurora borealis after a visit to Sweden in 1960. A natural spectacle in which electrons are refracted in the earth's magnetic field and which, for the artist, constituted a visible though fleeting sign of the invisible atomic energies which make up our universe. In this respect, Vantongerloo demonstrated a uniquely modern approach to art which responded to the unfolding discoveries of the cosmos and theoretical physics, as well as reflecting the startling scientific developments that he had experienced during his lifetime. 'Born in the era of the paraffin lamp', Vantongerloo had seen the arrival of the first electric tram and motor car as well as the advent of the gramophone and cinema, though perhaps the most thrilling of all was the launch of Sputnik in 1957, the very first time a satellite was launched into outer space and a radio signal beamed back to humankind.

For Vantongerloo, these developments demanded a new approach to art and its possibilities: 'Everything we have learned needs to be re-examined and the next generation can do something about it. The time of the paraffin lamp is past...We live now in the age of the atom, electromagnetism, radiation etc. Painting and sculpture as they used to be conceived, belong to the age of the paraffin lamp' (G. Vantongerloo, ibid., p. 52).

1946, the year in which the present work was executed, also coincided with the moment when Vantongerloo began to take up sculpture again after an eight year hiatus, executing models in wire and coloured plexiglass to convey his conceptualisation of universal, limitless space. In the course of his experiments he discovered the effect of prisms whereby, through the effect of refracted light, he could achieve pure, disembodied colour. In many respects, Spirale avec certaines taches works in conversation with these dynamic objects. The colours of the points and spiral recall the colours of the spectrum, while the sinuous line, free-floating in an expanse of white, echoes the delicate wire structures of the mobiles and sculptures themselves.

Ultimately Vantongerloo's compositions from the later period would remain conceptually elusive though tantalisingly suggestive. Crucially however, they reveal the continuity and refinement of the artist's key concerns from the time of his participation with De Stijl, in expressing universal laws and unity through abstract means. In a letter to the American sculptor Lilian Florsheim in 1960, Vantongerloo wrote, 'The things that I made in 1917 contain the same ideas as those I am making today, which are better expressed' (G. Vantongerloo, quoted in G. Brett, 'A longing for infinity', Georges Vantongerloo: A Longing for Infinity, op. cit., p. 18).

From the very beginning of his practice Vantongerloo was committed to a deeply authentic vision within his art. Indeed, even at the height of his involvement with De Stijl, he seems to have been guided by his own distinct principles and interpretation of sources. Subsequent criticism has acknowledged that even while apparently conforming to the strict rectilinear formats of the horizontal – vertical paintings, that Vantongerloo 'based his forms on ovoid, circular or parabolic principles, finding points along curved lines within which to locate straight lines and intersections' (J. Livingston, 'Introduction to Georges Vantongerloo' in Georges Vantongerloo. A traveling Retrospective Exhibition, Brussels, 1980, p. 12).

Although continuously engaged in his artistic quest for universal values throughout his lifetime, Vantongerloo's artistic output is extremely rare. As Max Bill explains, 'Vantongerloo's point of departure was not the wish to produce works of art but to present his ideas through colour and space' (M. Bill, (ed.), op. cit., p. 5). His dedication to writing as well as to scientific and mathematical study alongside his visual practice are testament to the seriousness of his work which, for Vantongerloo, stood outside of the transitory 'isms' defining modern art: 'My work represents a conception of creation and has nothing in common with so-called modern art' (G. Vantongerloo, quoted in G. Brett, (ed.), op. cit., p. 20). This did not prevent Vantongerloo from being an important influence on a generation of younger artists including Elsworth Kelly, who made a number of transformative visits to Vantongerloo's studio in 1950s, and the British Constructivists.

Aside from his experiments in painting and sculpture, and in contrast to many of his contemporaries, Vantongerloo was also an innovative designer and architect. While in Menton he designed a modernist villa and desk which he used in his studio, later devising projects for urban developments and an airport for which he received a medal from the 'Architectes Diplomés par le Gouvernement Français'. It is perhaps fitting then that the previous owner of Spirale avec certaines taches was the celebrated Belgian architect Georges Baines with whom Vantongerloo shared a long and productive friendship.

Baines, like Vantongerloo, was born in Antwerp, some 39 years after his artist friend. He studied architecture from 1943 - 1950 at the National Higher Institute for Architecture and Urban Planning in his native city, but was frustrated by the lack of modernist instruction that he received there. Following his formal training, he made research trips to Switzerland and Scandinavia in search of the avant-garde influences that would come to define his architectural practice. It was during these travels that he met the Swiss architect Alfred Roth who introduced him to a key group of abstract artists including Max Bill, Friedrich Vordemberge-Gildewart and Georges Vantongerloo, and it was through their pioneering developments in painting and sculpture that Baines developed his own architectural style in the modernist vein.

Baines established strong relationships with Bill, Vordemberge-Gildewart and Vantongerloo, evinced by numerous meetings and letters discussing the artists' work and their theoretical concerns. He was also actively engaged in the promotion of Vantongerloo's heritage after his death, contributing to posthumous exhibitions of his work as well as writing academic essays and articles. Meanwhile, Baines achieved much acclaim in his own country, winning the prestigious Den Ven prize for a private house in 1968 and later restoring Le Corbusier's first commission outside of France and only surviving building in Belgium, Maison Guiette, in the late 1980s - a building which was added to the UNESCO World Heritage list in 2016. In 1994 Baines received the Grand Prize for Belgian Architecture and just a few years later was knighted for his services to architecture.

The enduring impact of Vantongerloo's ideas and work today, as well as its significance within the developments of abstract art, mean that a large proportion of Vantongerloo's limited output resides in major museum collections across Europe and America. Spirale avec certaines taches, which has remained in private hands since its execution, is a key example from Vantongerloo's oeuvre and has been included in a number of notable surveys and retrospectives at institutions including the Reina Sofia and the Musées Royaux des Beaux-Arts de Belgique. For Vantongerloo, it was in the later works, of which Spirale avec certaines taches forms a part, that his ideas were best expressed, and it is in these works that we can observe which a truly original aesthetic. Today, his work continues to resound with audiences, speaking to the contemporary moment defined by science and technology and offering a profound understanding of human experience.

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